hw9 - xy = 1, the x-axis, and the two lines x = 1 and x =...

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Math 53 Homework 9 Due Wednesday 10/27/10 in section (The problems in parentheses are for extra practice and optional. Only turn in the underlined problems.) Tuesday 10/19: Change of variables in double integrals Read: section 15.9 to the end of p. 1018. Work: 15.9: (1), 3 , (7), 11 , (13), 15 , 19 , (20). Problem 1 below. Thursday 10/21: Triple integrals in rectangular and cylindrical coordinates Read: sections 15.6, 15.7. Work: 15.6: (3), 9 , (11), 15 , (17), 21 , (27), 33 , 35 , (37), (41), 44 , (51), 52 . 15.7: (1), 9 , 15 , (17), 18 , (21), 22 , (23), (24). Problem 2 below. (Note: a couple of the problems in 15.6 are best done in cylindrical coordinates. Use your judgment.) Problem 1. Using the coordinate change u = xy , v = y/x , set up an iterated integral for the polar moment of inertia of the region bounded by the hyperbola
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Unformatted text preview: xy = 1, the x-axis, and the two lines x = 1 and x = 2. Choose the order of integration which makes the limits simplest. Problem 2. The picture shows the portion of the solid formed by the intersection of the solid cylinders y 2 + z 2 1 and x 2 + z 2 1 (two cylinders of radius 1, centered on the x-axis and on the y-axis respectively) which lies in the Frst octant ( x 0, y 0, z 0). (The front face is a portion of the cylinder x 2 + z 2 = 1, while the right face is part of the cylinder y 2 + z 2 = 1.) ind the volume and the centroid ( x, y, z ) (= center of mass with uniform density = 1) of the pictured solid. (Hint: the integral is easier to set up in the order dx dy dz )....
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